A valve drive of said type can be gathered from JP 2000161025 A which is considered as being generic. Proposed in said document is a rocker arm valve drive whose valve play adjustment takes place by exchanging the support element for a different support element with an installation height corresponding to the nominal valve play. For this reason, and also on account of a lack of indications in said document which allow conclusions to be drawn regarding a dimensional relationship, with regard to the valve play, of the support element and the rocker arm in the non-assembled state outside the cylinder head, a person skilled in the art arrives at the result that even the initial assembly of said valve drive into the cylinder takes place in a conventional manner. On account of the complex kinematic conditions of the rocker arm valve drive, the level of valve play is determined or controlled here by means of direct measurement or testing of the free travel of the rocker arm relative to the cam or the gas exchange valve. A prerequisite for this is however that the valve drive is situated in a very advanced assembly state of the cylinder head, so that with the knowledge of the determined actual valve play or its deviation from the nominal valve play, the actual valve play adjustment, which is then often necessary, to the nominal valve play can take place only after renewed disassembly of the valve drive for the purpose of exchanging the support element. Said intermediate step of the provisional assembly of the valve drive into the cylinder head is however associated with a considerable level of time expenditure, and consequently with high production costs, in particular within the context of mass production assembly.